Question: Vanessa is 6 years older than Kevin. Eighteen years ago, Vanessa was 3 times as old as Kevin. How old is Kevin now?
We can use the given information to write down two equations that describe the ages of Vanessa and Kevin. Let Vanessa's current age be $v$ and Kevin's current age be $k$ The information in the first sentence can be expressed in the following equation: $v = k + 6$ Eighteen years ago, Vanessa was $v - 18$ years old, and Kevin was $k - 18$ years old. The information in the second sentence can be expressed in the following equation: $v - 18 = 3(k - 18)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $k$ , it might be easiest to use our first equation for $v$ and substitute it into our second equation. Our first equation is: $v = k + 6$ . Substituting this into our second equation, we get the equation: $(k + 6)$ $-$ $18 = 3(k - 18)$ which combines the information about $k$ from both of our original equations. Simplifying both sides of this equation, we get: $k - 12 = 3 k - 54$ Solving for $k$ , we get: $2 k = 42$ $k = 21$.